The Lie group G = GL(n, R) is an open submanifold of the vector space Mnxn of nxn real matrices, hence the tangent space TG is naturally identified with Mixn. Let VEM, TG, and let v Lie(G) denote its extension to a left-invariant vector field on G. For i, j {1,...,n}, let fij EC(G) denote the function which maps a matrix to its i, j entry. Compute the smooth function vfi; E C (G) by giving an explicit formula for (vfij) (8) in terms of the matrix entries gke of g. Note that X f denotes the action of a vector field X on a smooth function f as a derivation. The Lie group G = GL(n, R) is an open submanifold of the vector space Mnxn of nxn real matrices, hence the tangent space TG is naturally identified with Mixn. Let VEM, TG, and let v Lie(G) denote its extension to a left-invariant vector field on G. For i, j {1,...,n}, let fij EC(G) denote the function which maps a matrix to its i, j entry. Compute the smooth function vfi; E C (G) by giving an explicit formula for (vfij) (8) in terms of the matrix entries gke of g. Note that X f denotes the action of a vector field X on a smooth function f as a derivation